Subgroups — C₁₁×#7537 #14584730

Order 2816.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₁₆	—	2	1	no	—
5	C₁₁×D₃₂	—	2	1	no	—
6	C₁₁×D₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₁×#366	—	2	1	no	—
9	C₁₁×C₆₄	—	2	1	no	—
10	C₂×C₁₁×D₈	—	4	1	no	—
11	C₁₁×D₁₆	—	2	2	no	—
12	C₁₁×D₁₆	—	4	1	no	—
13	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
14	C₁₁×#107	—	4	1	no	—
15	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₃₂	D₄	1	1	yes	characteristic
17	#7537	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×D₄×C₁₁	—	8	1	no	—
19	C₁₁×D₈	—	4	2	no	—
20	C₁₁×D₈	—	8	1	no	—
21	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
22	C₁₁×C₄⋊C₄	—	8	1	no	—
23	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×D₃₂	C₂×C₁₁	1	1	yes	characteristic
26	C₂×C₆₄	C₂×C₁₁	1	1	yes	characteristic, complemented
27	#1423	C₂×C₁₁	1	1	yes	characteristic, complemented
28	C₂³×C₁₁	—	16	1	no	—
29	D₄×C₁₁	—	8	2	no	—
30	D₄×C₁₁	—	16	1	no	—
31	C₂×C₄×C₁₁	—	16	1	no	—
32	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
33	C₈×C₁₁	#102	1	1	yes	characteristic
34	C₈×C₁₁	SD₃₂	1	1	yes	characteristic
35	C₂×D₁₆	—	2	1	no	—
36	D₃₂	—	2	1	no	—
37	D₃₂	C₄×C₁₁	1	2	yes	complemented
38	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
39	#366	—	2	1	no	—
40	C₆₄	—	2	1	no	—
41	C₂²×C₁₁	—	16	2	no	—
42	C₂²×C₁₁	—	32	1	no	—
43	C₂²×C₁₁	—	32	1	no	—
44	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
45	C₄×C₁₁	—	32	1	no	—
46	C₄×C₁₁	#357	1	1	yes	characteristic
47	C₄×C₁₁	SD₆₄	1	1	yes	characteristic
48	C₂×D₈	—	4	1	no	—
49	D₁₆	—	2	2	no	—
50	D₁₆	—	4	1	no	—
51	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
52	#107	—	4	1	no	—
53	C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
54	C₃₂	D₄×C₁₁	1	1	yes	characteristic
55	C₂×C₁₁	—	32	2	no	—
56	C₂×C₁₁	#1415	1	1	yes	characteristic
57	C₂×C₁₁	D₆₄	1	1	yes	characteristic
58	C₂×C₁₁	SD₁₂₈	1	1	yes	characteristic
59	C₂×D₄	—	8	1	no	—
60	D₈	—	4	2	no	—
61	D₈	—	8	1	no	—
62	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
63	C₄⋊C₄	—	8	1	no	—
64	C₁₆	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
65	C₁₆	C₁₁×SD₁₆	1	1	yes	characteristic
66	C₁₁	#7537	1	1	yes	characteristic, direct product factor, Sylow
67	C₂³	—	16	1	no	—
68	D₄	—	8	2	no	—
69	D₄	—	16	1	no	—
70	C₂×C₄	—	16	1	no	—
71	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
72	C₈	C₁₁×#102	1	1	yes	characteristic
73	C₈	C₁₁×SD₃₂	1	1	yes	characteristic
74	C₂²	—	16	2	no	—
75	C₂²	—	32	1	no	—
76	C₂²	—	32	1	no	—
77	C₂²	C₁₁×D₃₂	1	1	yes	characteristic
78	C₄	—	32	1	no	—
79	C₄	C₁₁×#357	1	1	yes	characteristic
80	C₄	C₁₁×SD₆₄	1	1	yes	characteristic
81	C₂	—	32	2	no	—
82	C₂	C₁₁×#1415	1	1	yes	characteristic
83	C₂	C₁₁×D₆₄	1	1	yes	characteristic
84	C₂	C₁₁×SD₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	D₃₂
commutator	C₃₂	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₁
prime radical	C₂×C₁₁×D₃₂	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ C₂×C₁₁×C₃₂ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₁×C₆₄	C₂	semidirect
3. C₁₁×#1423	C₂	semidirect
6. C₁₁×D₃₂	C₄	semidirect
17. #7537	C₁₁	direct (N × H)
26. C₂×C₆₄	C₂×C₁₁	semidirect
27. #1423	C₂×C₁₁	semidirect
37. D₃₂	C₄×C₁₁	semidirect
66. C₁₁	#7537	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×D₃₂	2
C₂×C₁₁×C₆₄	2
C₁₁×#1423	2
#7537	11

Subgroups — C11×#7537 #14584730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7537 #14584730